- Thread starter
- #1
DreamWeaver
Well-known member
- Sep 16, 2013
- 337
Just for fun, eh...? 
For \(\displaystyle z \in \mathbb{R}\), and \(\displaystyle m \in 2\mathbb{N}+1\), show that:
\(\displaystyle \frac{\tan mz}{\tan z}=\prod_{j=1}^{ \lfloor m/2 \rfloor } \tan\left(\frac{j\pi}{m}+z\right) \tan\left(\frac{j\pi}{m}-z\right) \)

For \(\displaystyle z \in \mathbb{R}\), and \(\displaystyle m \in 2\mathbb{N}+1\), show that:
\(\displaystyle \frac{\tan mz}{\tan z}=\prod_{j=1}^{ \lfloor m/2 \rfloor } \tan\left(\frac{j\pi}{m}+z\right) \tan\left(\frac{j\pi}{m}-z\right) \)